Question
$P\ v\ Q$
$Q$
$\therefore \sim\ P$
$Q$
$\therefore \sim\ P$
| Support Statement | The resulting statement | ||||||
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | ||
| $P$ | $Q$ | $\sim P$ | $P\ v\ Q$ | $(P\ v\ Q)\ \&\ Q$ | $\sim P$ | ||
| $1$ | $T$ | $T$ | $F$ | $T$ | $T^*$ | $F^*$ | |
| $2$ | $T$ | $F$ | $F$ | $T$ | $F$ | $F$ | |
| $3$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ | |
| $4$ | $F$ | $F$ | $T$ | $F$ | $F$ | $T$ | |
| $1 (\sim )$ | $1, 2(v)$ | $4, 2 (\&)$ | As $3$ | ||||
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| $(A \rightarrow B) \rightarrow R$ |
| $R \rightarrow S$ |
| $(A \rightarrow B)\ \&\ T$ |
| $S\ \&\ T$ |
| $A\ v\ B$ |
| $\sim\ A\ \&\ C$ |
| $\therefore (B\ v\ \sim\ D)\ \&\ C$ |
| $G \rightarrow J$ |
| $J \rightarrow K$ |
| $(G \rightarrow K) v (J \rightarrow L)$ |
| $L \rightarrow M$ |
| $\therefore (J \rightarrow M) v\ Q$ |
| $(A\ \rightarrow\ E)\ \&\ (D\ \rightarrow\ F)$ |
| $B\ \&\ (A\ v\ D)$ |
| $(E\ v\ F)\ \rightarrow\ (B\ v\ D)$ |
| $\sim\ B$ |
| $\therefore D$ |